Since you are the only owner, we look at your basis and your exclusion only. (If you were joint owners this would be calculated differently.)
Your basis is either $63K plus $50K; or $63K plus $100K. The amount you paid to buy out your ex is added to your original basis. Assuming that you have a legal debt for the other $50K that wasn't paid yet, you can add the full $100K to your basis even though it wasn't actually paid in money. (Just as you get credit for the full $63K in original purchase price even though you probably put 10-20% down and financed the rest.) I disagree with the above about the interest—don't think the interest you owe adds to your basis.
As mentioned above, your capital gain is 338K minus your basis of $163K = $175K. Since you lived in the home as your main home for at least 2 years of the past 5 years, you can exclude the first $250K of gain from taxation, so you won't owe any federal capital gains tax. You don't even have to report the sale on your tax return unless you get a form 1099-S at the closing.
If you needed to reduce your gain calculation, you can adjust your basis by the cost of any permanent improvements and certain non-deductible closing costs from 1999 like inspections and surveys; and you can reduce the selling price by the commission and by legal fees, inspections, and other selling costs that you pay (but not repairs, painting, etc.) Although, since your gain is less than the $250,000 exclusion, accounting for these items probably won't make a difference.
